Visual Plane
every picture states the point it is correct from
Field

Systems that kept the measure

A removed roof, a ground plane tilted into the picture, a figure assembled from the aspect that identifies each part. Every one of them gives up the single station point and buys something exact with it — a floor a reader can measure with one ruler, a depth scale that does not bunch, a picture in which nothing is edge-on.
parallel, 52° above the ground56% · 56% · 56%one eye, 14.5 m away49% · 56% · 49%a square metre of floor varies 1.000× against 1.535×spread across rooms: 0 against 6.2 points

What the removed roof buys

The Japanese convention of drawing an interior with its roof lifted off is usually explained as a way of seeing inside. What it actually buys is uniformity — every room reports the same share of its floor, to the last sample, where the eye that frames the same building reports three different numbers.

 parallel, 52° above the ground56% · 56% · 56%one eye, 14.5 m away49% · 56% · 49%a square metre of floor varies 1.000× against 1.535×spread across rooms: 0 against 6.2 points

Measuring a room off the page

A perspective picture of a floor has to be rectified before anything on it can be measured, and the rectification is a fit that amplifies the marking error. An oblique picture of the same floor is already rectified — the page is the plan, at one scale, and a ruler on the paper is a ruler on the ground.

 0100200204060distance of the object, metresits drawn height, pxa pinholean oblique systemdrawn height of a fixed object against its distance20.0× against 1.000

A picture with no size–distance signal

In a system with no diminution the drawn size of an object falls at exactly zero pixels per metre, so nothing in the picture says how far away anything is. Depth has to be carried by something else, and what carries it is height on the page — linearly, and without a horizon.

 a camera looking downthe carpet is true, the people are nota camera looking levelthe people are true, the carpet is notthe two views a miniature is assembled from90° apart, exactly

A carpet and the people on it

A Persian miniature draws the ground as though from above and the figures standing on it as though from in front. The two views want optical axes exactly ninety degrees apart, and the plan view does not shorten a standing figure — it replaces its height with its distance from the point under the eye.

 head0.668profile — the outline that names a faceeye0.669frontal — an eye in profile is a wedgeshoulders0.669frontal — the width that says two armslegs0.668profile — a stride is a side viewpond0.326plan — a rectangle of water is a rectangle1.000 — what its own aspect keepsshare of each part that reaches the picture, from the best single direction|d · n| for each part3.000 of 5, swept and in closed form

Assembled from several views

An Egyptian relief takes each part of a figure from the direction that identifies it — head in profile, eye and shoulders frontal, a pond in plan. What that buys is exactly measurable: any single viewing direction keeps at most √k of k perpendicular aspects, so the best compromise view retains 58% of each.

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